Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
478 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10604695 | C2 | semidirect |
| 5. #10604687 | C2 | semidirect |
| 6. #10604291 | C2 | semidirect |
| 7. #10604271 | C2 | semidirect |
| 45. C2×#687 | C8 | semidirect |
| 365. C5 | #9667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65047 | 2 |
| #10604932 | 2 |
| #10604922 | 2 |
| #10604695 | 2 |
| #10604687 | 2 |
| #10604291 | 2 |
| #10604271 | 2 |
| #9667 | 5 |